Essays on exponential series estimation and application of copulas in financial econometrics

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Abstract

This dissertation contains three essays. They are related to the exponential series
estimation of copulas and the application of parametric copulas in financial
econometrics. Chapter II proposes a multivariate exponential series estimator (ESE) to
estimate copula density nonparametrically. The ESE attains the optimal rate of
convergence for nonparametric density. More importantly, it overcomes the boundary
bias of copula estimation. Extensive Monte Carlo studies show the proposed estimator
outperforms kernel and log-spline estimators in copula estimation. Discussion is
provided regarding application of the ESE copula to Asian stock returns during the
Asian financial crisis. The ESE copula complements the existing nonparametric copula
studies by providing an alternative dedicated to the tail dependence measure.
Chapter III proposes a likelihood ratio statistic using a nonparametric exponential
series approach. The order of the series is selected by Bayesian Information Criterion
(BIC). I propose three further modifications on my test statistic: 1) instead of putting
equal weight on the individual term of the exponential series, I consider geometric and exponential BIC average weights; 2) rather than using a nested sequence, I consider all
subsets to select the optimal terms in the exponential series; 3) I estimate the likelihood
ratio statistic using the likelihood cross-validation. The extensive Monte Carlo
simulations show that the proposed tests enjoy good finite sample performances
compared to the traditional methods such as the Anderson-Darling test. In addition, this
data-driven method improves upon Neyman’s score test. I conclude that the exponential
series likelihood ratio test can complement the Neyman’s score test.
Chapter IV models and forecasts S&P500 index returns using the Copula-VAR
approach. I compare the forecast performance of the Copula-VAR model with a classical
VAR model and a univariate time series model. I use this approach to forecast S&P500
index returns. I apply a modified Diebold-Mariano test to test the equality of mean
squared forecast errors and utilize a forecast encompassing test to evaluate forecasts. The
findings suggest that allowing a more flexible specification in the error terms using
copula tends improve the forecast accuracy. I also demonstrate combined forecasts
improved forecasts accuracy over individual models.